Statistics · Practice

Standard Deviation — Exercises

Graded practice problems from foundations to advanced. Enter your answer and press Check.

Foundations

Problem 1

What is the standard deviation of the data set $5, 5, 5, 5$ ?

Problem 2

For $1, 2, 3, 4, 5$ find the variance (population).

Problem 3

For $1, 2, 3, 4, 5$ find the standard deviation (population).

Problem 4

Find the population standard deviation of $0$ and $10$ .

Problem 5

A data set has $\sigma = 10$ . Every value is increased by $5$ . What is the new $\sigma$ ?

Problem 6

A data set has $\sigma = 10$ . Every value is multiplied by $2$ . What is the new $\sigma$ ?

Problem 7

A distribution has $\mu = 60$ , $\sigma = 5$ . Find the $z$ -score for $x = 70$ .

Problem 8

A distribution has $\mu = 60$ , $\sigma = 5$ . Find $x$ when $z = 1$ .

Problem 9

Find the sample standard deviation of $1, 2, 3, 4, 5$ .

Problem 10

In a normal distribution, approximately what percentage of data falls within 1 standard deviation of the mean?

Problem 11

The standard deviation of a distribution is $1$ . What is the variance?